An improved Born approximation for volume scattering and absorption of electromagnetic radiation by a nonmagnetic, granular medium of small grains with large dielectric contrast is formulated. In this low-frequency approximation it is assumed that the permittivity of the medium is given by the effective-medium theory of Polder and van Santen which also provides an expression for the internal field. The model is used to derive formulas for the scattering and absorption coefficients of freely arranged spheres and spherical shells. In addition, measured dielectric properties are used to derive relevant model data of dry snow. In contrast to the conventional Born approximation, the results reproduce Rayleigh scattering for a single particle, and for a dense medium the scattering coefficient shows a nonlinear behavior with increasing density, comparable to the dense-medium radiative transfer theory. Characteristic differences of the spectra of the scattering coefficients result for the different particle types.